Question

A man when asked how many hens and cows did he have replied that the animals had 100 eyes and 120 legs. Find the number of hens and cows.

Answer 1

Suppose the number of hens are x and number of cows are y.
Since there are 100 eyes and each animal has 2 eyes which means total number of animals are $\frac{100}{2}$ i.e. 50
so total number of animals = $x+y=50...\left(\mathrm{i}\right)$
And since cow has 4 legs and each hen has 2 legs;
So total number of legs = $2x+4y=120$
$$\begin{gathered} \Rightarrow 2\left(x+2y\right)=120 \\ \Rightarrow x+2y=60...\left(\mathrm{ii}\right) \end{gathered}$$
Solving (i) and (ii) we get;
$$\begin{gathered} x+y-x-2y=50-60 \\ \Rightarrow -y=-10 \\ \Rightarrow y=10 \end{gathered}$$
Then; $x=50-10=40$
Therefore total number of hens are 40 and number of cows are 10.